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The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then find the other number.

Sagot :

Given:

The LCM of two numbers is 14 times their HCF.

The sum of LCM and HCF is 600.

One number is 280.

To find:

The other number.

Solution:

Let HCF of two numbers be x.

The LCM of two numbers is 14 times their HCF.

LCM = 14x

The sum of LCM and HCF is 600.

[tex]14x+x=600[/tex]

[tex]15x=600[/tex]

[tex]x=\dfrac{600}{15}[/tex]

[tex]x=40[/tex]

So, HCF = 40 and the LCM is

[tex]LCM=14(40)[/tex]

[tex]LCM=560[/tex]

We know that, if a and b are two numbers, then

[tex]a\times b=LCM(a,b)\times HCF(a,b)[/tex]

One number is 280.

[tex]280\times b=560\times 40[/tex]

[tex]b=\dfrac{560\times 40}{280}[/tex]

[tex]b=2\times 40[/tex]

[tex]b=80[/tex]

Therefore, the other number is 80.

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